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A NEW RESOLUTION 




OF THB 



flkuiete^ aiil SfeliDce 



OF THE 



'©^Ti)®lF ®@#li)i 



BY COMMON ABITHMETIC, 



ACCOMPANIED WITH AN 



^f|iKt cf i\t Variations of i|e ^skonoMfw, 




AND A 



DISPROOF OF THE NEWTONIAN THEORY 



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BY WM. ISAACS LOOMIS, 

Piermont, Mochland Co,, JV, T, 




T. HOLMAN, PRINTER, CORNER CENTRE AND WHITE STREETS. 

1868. 

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Entered, according to Act of Confess, in the year 1868, - 
BY WM. ISAACS LOOMIS, 

s 

In the Clerk's Office of the District Court of the United States, for the 
Southern District of New York. 



Thomas Holman, 
Printer and Stereotyper. 






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TRUTHS. 



Proverbs, Chapter 111., Verses 5, 6. 

1. " Trust in the Lord with all thy heart ; and 
lean not unto thine own understanding. In all 
thy ways acknowledge him, and he shall direct 
thy paths.'' 

2. Open to men the right path, aided by God- 
given and God- directed reason, and then the 
humblest of our race may become familiar with 
the works of God. 

A comparison of my manner of determining the 
diameters and distances of the heavenly bodies 
with others. 

T. Dick's rule and example to find the real 
diameter of the moon is given by him in the third 
volume of his works, on p. 144 of Celestial Scenery : 

"As radius : is to C G, the distance of the moon, 
238,800 miles, : : so is the sine of A C.G, 15' 43" : 
to the number of miles contained in the moon's 
semi-diameter, AG=10914, which, being doubled, 
gives 2,183 miles as the diameter of the moon. 

2dterm— C Gr=238,800— Log.... 5.378028 

3d term— sine of A G, 15' 43" . . 7.660059 



1st term — radius 



Semi-diameter of the moon I.OQIJ: 

2 



13.038087 
10.000000 

3.038087 




2,183" 



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(& 



Mj rule and example to find in the fourth term 
of a simple proportion the real diameter of the 
moon : 

As the angle of the equatorial horizontal par- 
allax of the moon 57' 5" : is to her apparent 
diameter of 31' 2G'' : : so is the base line of the 
parallax 3,963 miles : to a fourth term in simple 
proportion in common arithmetic = the moon's 
real diameter. 

De7no?istration. — As 57' 5" : 31' 26" : : 3,963 
miles : 2,182 miles, which is the moon's real di- 
ameter. 

Planetary Distance. 

After the manner of Kepler, to find the distance 
of any planet from the sun. 

Rule. 

Divide the square of the planet's sidereal 
revolution round the sun by the square of the 
earth's sidereal revolution, and multiply the cube 
root of the quotient by the earth's mean distance 
from the sun. In the use of this rule to find the 
distance of the planet Mercury from the sun by 
common arithmetic, or by logarithms, Burritt, 
on p. 160 of his Geography of the Heavens, says : 
"He need not think himself a 6??/// scholar, if by 
the former method he comes to the true result in 
FIVE HOURS ; nor remarkably quick, if by the lat- 
ter he comes to it mjive minutes,^ ^ 

N. B. — My distance of Mercury was obtained in 
less than five minutes by common arithmetic. 
(See the example on p. 93.) 






moon's distance by the author's system. 87 

T. Dick's Moon's Distance by Logarithms. 

2d term — 3,965=the earth's semi- 
diameter 3.598243 

3d term—radius 10.000000 




13.598243 
1st term— sine of 57' 5" 8.220215 




M C, distance of moon, 238,800 miles ^ 5.378028 

Moon's Distance by the Author's Method. 

As the angle of the moon's parallax of 57' 5" : 
is to the circle in degrees 360*^ :: so is the base 
line of the parallax 3,963 miles : to the circle in 
miles 1,499,576, the semi-diameter of which is 
238,665 miles, which is the moon's mean dis- 
tance from the earth. (See my rules on diameters 
and distances.) 

The advantages of my method are : Firsts brev- 
ity in operation, astonishingly so, in finding the 
diameters of the heavenly bodies. Second, inde- 
pendent of a knowledge of trigonometry and log- 
arithms, with a very limited knowledge of common 
arithmetic, these problems to find the diameters and 
distances of the heavenly bodies may be solved. 

Lest any should stumble because my results 
vary somewhat from those of the astronomers, it 
may not be amiss to notice the difference between 
some of the least and greatest diameters of the 
planets which astronomers have assumed to be 
very near approximations to the truth. 

Sir John W. Herschel makes the diameter of 
Mercury 156 miles more than Burritt states it to 
be, and 540 miles more than Ferguson's diameter. 
Between Ferguson's and Bartlett's estimates of the 






-Oo^ 



APPARENT DIAMETERS. 



diameter of Yenus there is a difFereDce of 530 
miles. 0. M. Mitcliel's value of Jupiter's real 
diameter is 11,164 miles more than that given by 
Ferguson, and 5,164 miles more than Herschel's 
diameter. E. H, Burritt's computation of the di- 
ameter of Saturn exceeds Ferguson's by the enor- 
mous sum of 14,952 miles. Sir J. W. Herschel 
estimated the diameter of Keptune to be 7,890 
miles greater than 0. M. Mitchel's estimate. 

Diameters of Heavenly Bodies. 

I will give the angles or arcs, which are the 
measures of the angles of certain parallaxes of 
heavenly bodies, their apparent diameters, base 
line of the parallaxes, and the rule to determine 
their real diameters by simple proportion. 

Moon's angle or arc of parallax. ... 57' 5" 




Sim's 


(( 






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8".6 


Mercury's 
Yenus' 


.1 










14" 
31" 


Mars' 


ii 






a 




16" 


Jupiter's 
Saturn's 


11 






n 




2" 
1" 


Uranus' 


it 






a 




0".4722 


ISTeptune's 


u 






a 


0".2967 






Apparent 


Diameters. 




Moon's ap] 
Sun's 


3arent 

u 
11 
(< 
(( 
li 
u 
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diamete 


T 


31' 26" 
32' 12".6 


Mercury's 
Yenus' 




11" 




61".2 


Mars' 




16".61 


Jupiter's 
Saturn's 




47" 




18" 


Uranus' 




4" 


Neptune's 




2".5 



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DEMONSTRATIONS, 





The equatorial semi- diameter of the earth is the 
base Hue of all equatorial horizontal parallaxes, 
the linear measure being 3,963 miles. 

Rule. 

As the angle of the equatorial horizontal paral- 
lax of a heavenly body : is to its apparent diame- 
ter : : so is the base line of the parallax : to the 
real diameter pf the heavenly body. 

Demonstrations. 

DIAMETER OF THE MOON. 

1. As the angle of the Moon's paral- 

lax 57' 5" 

Is to her apparent diameter 31' 26" : 

So is the base line of the parallax, 3,963 miles 
To the real diameter of the moon, 2,182 miles 

DIAMETER OF THE SUN. 

2. As the angle of the Sun's parallax, S".Q 

Is to his apparent diameter 31' 12".6 : 

So is the base line of the parallax, 3,963 miles 
To the real diameter of the sun. 890,569 miles 

DIAMETER OF MERCURY. 

3. As the angle of Mercury's parallax, 14" 

Is to his apparent diameter 11" : 

So is the base line of the parallax, 3,963 miles 

To the real diameter of Mercury, 3,113 miles 

DIAMETER OF VENUS. 

4. As the angle of Yenus' parallax, 31" 

Is to her apparent diameter 61".2 : 

So is the base line of the parallax, 3.963 miles 

To the real diameter of Yenus.. . 7,823 miles 








ja&i 



DEMONSTRATIONS. 



DIAMETER OF MARS. 




5. As the angle of Mars' parallax.. 16" 

Is to his apparent diameter. .... 16".61 : 

So is the base line of the parallax, 3,963 miles 

To the real diameter of Mars 4,114 miles 



DIAMETER OF JUPITER. 



2" 



6. As the angle of Jupiter's parallax, 

Is to his apparent diameter 47" : 

So is the base line of the parallax, 3,963 miles 

To the real diameter of Jupiter.. 93,130 miles 



DIAMETER OF SATURN. 



1" 



7. As the angle of Saturn's parallax. 

Is to his apparent diameter 18" : 

So is the base line of the parallax, 3,963 miles 
To the real diameter of Saturn. . 71,334 miles 

DIAMETER OF URANUS. 

8. As the angle of Uranus' parallax, 0".4722 

Is to his apparent diameter 4" : 

So is the base line of the parallax, 3,963 miles 

To the real diameter of Uranus. . 33,571 miles 

DIAMETER OF NEPTUNE. 

9. Asthe angle of Neptune's parallax, 0".2967 

Is to his apparent diameter 2".5 : 

So is the base line of the parallax, 3,963 miles 
To the real diameter of Neptune, 33,392 miles. 

BY MY METHOD. 

The Moon's real diameter is 2,182 miles. 

" Sun's " " 890,569 *' 

Mercury's ' '' " 3,113 

Yenus' '' " 7,823 

Mars' " *' 4,114 



^§^ 



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DISTANCES OP THE PLANETS. 





Jupiter's real diameter is 93,130 miles. 

Saturn's " '' 71,334 '' 

Uranus' '' " , 33,571 " 

Neptune's '' '' 33,392 '' 

pistances of the Planets. 

1. The sines and tangents of the angles of the 
equatorial horizontal parallaxes of the sun and 
planets differ so insensibly from each other, that, 
without liability to error, the linear measure of the 
arc of any one of these angles may, without further 
labor, be assumed to be the same as the linear 
measure of the tangent of the angle. 

2. In the projection of an equatorial horizontal 
parallax there is exhibited a right-angled triangle, 
the base line of which is the equatorial semi-diame- 
ter of the earth, and its perpendicular leg represents 
the distance. 

3. Because the perpendicular leg of any right- 
angled triangle is the semi-diameter of a circle, an 
arc of which is the measure of the angle at the ver- 
tex, it is evident that, given the degree and linear 
measure of the arc of the angle, the perpendicular 
leg of any right-angled triangle may be determined 
in the same way that we determine the semi-diame- 
ter of a circle, given the degrees and linear measure 
of an arc of a circle to find its semi-diameter. 

Example. 

To find the perpendicular leg of a right-angled 
triangle : Griven the angle at the vertex 12°, and 
the linear measure of the arc of the angle 12 inches. 

Demonstration.— As 12° : 360° : : 12 inches : 360 
inches^3.14159=114.59-^-2=57.29 inches, which: 
is the linear measure of the required leg. 

— rpar 



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92 



DEMONSTRJlTIONS. 



This method may be employed to find the dis- 
tances of the heavenly bodies, substituting the 
linear measure of the base line of the parallax for 
that of the arc. 




Rule, 

As the angle of any equatorial horizontal paral- 
lax : is to the circle in degrees : : so is the linear 
measure of the base line of the parallax : to the 
linear measure of the circle, the semi- diameter of 
which is the perpendicular leg of the right-angled 
triangle of the parallax. 




Demonstrations. 

DISTANCE OF THE MOON. 

1. As the angle of the Moon's parallax, 57' 5" 

Is to the circle in degrees 360° : 

So is the base line of the parallax, 3,963 miles 
To the circle in miles 1,499,576-^3.14159= 

477,330-^2=238,665 miles, which is the moon's 

mean distance. 




DISTANCE OF THE SUN. 

2. As the angle of the Sun's parallax, 8".Q 

Is to the circle in degrees 360° : 

So is the base line of the parallax, 3,963 miles 
To the circle in miles, 597,214.853.7209313-^ 
3.1415926=190,099,404, which is the diameter of 
the earth's orbit, -^2=95,049,702 miles, the hnear 
measure of the perpendicular leg of the right-angled 
triangle projected in the sun's equatorial horizontal 
parallax, and is the mean distance of the sun from 
the earth. 



i 





DEMONSTRATIONS. 





DISTANCE OF MERCURY. 

3. As the angle of Mercury's parallax, 14" 

Is to the cuxle in degrees 360° : 

So is the base line of the parallax, 3,963 miles 
To the circle in miles 386,860,571.4285714, the 

semi-diameter of which is 58,387,674 miles, and is 
the distance of Mercury from the earth at the time 
of his inferior conjunction. Subtract this distance 
of the planet from the earth from the earth's mean 
distance from the sun, and the remainder, 36,662,028 
miles, is Mercury's distance from the sun. 

DISTANCE OF YENUS. 

4. As the angle of Yenus' parallax, 31" 

Is to the circle in degrees 360° : 

So is the base line of the parallax, 3,963 miles 
To the circle in miles 165,678,967.7419354, the 

semi- diameter of which is 26,368,627, and is the 
distance of Yenus from the earth at the time of her 
inferior conjunction. Subtract this distance of the 
planet from the earth from the earth's mean dis- 
tance from the sun, and the remainder, 68,681,075 
miles, ii the distaiice of Yenus from the sun. 

DISTANCE OF MARS. 

5. As the angle of Mars' parallax . . 16" 

Is to the circle in degrees 360° : 

So is the base line of the parallax, 3,963 miles 
To the circle in-miles 321,003,000.0000000, the 

semi-diameter of which is 51,089,215 miles, and is 
the distance of Mars from the earth at the time of 
his opposition. Add this distance of the planet 
from the earth to the earth's mean distance from 
the sun, and the sum 146,138,917 miles is the dis- 
tance of Mars from the sun. 






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I! 

i 





DEMONSTRATIONS. 



DISTANCE OF JUPITER. 



6. As the angle of Jupiter's parallax, 

Is to the circle in degrees 

So is the base line of the parallax, 



2" 



360°: : 
3,963 miles : 
To the circle in miles 2,568,024,000.0000000, 
the semi-diameter of which is 408,713,720 miles, 
and is the distance of Jupiter from the earth at the 
time of his opposition. Add this distance of the 
planet from the earth to the earth's mean distance 
from the sun, and the sum, 503,763,422 miles, is the 
distance of Jupiter from the sun. 



DISTANCE OF SATURN. 



1'': 



7. As the angle of Saturn's parallax. 

Is to the circle in degrees 360° : : 

So is the base line of the parallax, 3,963 miles : 
To the circle in miles 51,360,480,000.0000000, 

the semi-diameter of which is 817,427,425 miles, 
and is the distance of Saturn from the earth at the 
time of his opposition. Add this distance of the 
planet to the earth's mean distance from the sun, 
and the sum 912,477,123 miles is the distance of 
Saturn from the sun. 

DISTANCE OF URANUS. 

8. As the angle of the parallax of 

Uranus , 0".4722 : 

Is to the circle in degrees 360° : : 

So is the base line of the parallax, 3,963 miles : 

To the circle in miles 10,876,848,793.0000000, 

the semi-diameter of which is 1,731,105,871 miles, 

and is the distance of Uranus from the earth at the 

time of his opposition. Add this distance of the 



""SBsr 



— C 




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SOLAR DISTANCES OF THE PLANETS. 




planet from the earth to the earth's mean distance 
from the sun, and the sum, 1,826,155,573 miles, is 
the distance of Uranus from the sun. 

DISTANCE OF NEPTUNE. 

9. As the angle of the parallax of 

Neptune 0".2967 

Is to the circle in degrees 360° : 

So is the base line of the parallax, 3,963 miles 
To the circle in miles 17,310,576,339.7371028, 
the semi-diameter of which is 2,755,063,855 miles, 
and is the distance of Neptune from the earth at 
the time of his opposition. Add this distance of 
the planet from the earth to the earth's mean dis- 
tance from the sun, and the sum, 2,850,113,557 
miles, is the distance of Neptune from the sun. 

Solar Distances of the Planets. 



Mercury's solar distance 
Yenus' 



it 



Earth's 

Mars^ 

Jupiter's 

Saturn's 

Uranus' 

Neptune's 

The distances of the 



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II 



tt 



tt 



<< 



tt 



36,662,028 miles. 

68,681,075 '' 

95,049,702 '' 

146,138,917 '' 

503,763,422 '' 

912,477,123 '' 

1,826,155,573 ''" 

2,850,113,557 " 

heavenly bodies may be 



found by Division. I will exhibit two examples. 



Rule. 




Divide the linear measure of the tangent of the 
angle of the parallax by the circular measure of 
the arc of the parallax, and the quotient will be 
the term required. 



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96 


DISTANCE OP THE SUN BY DIVISION. 


< 



Distance of the Moon by Division. 

1. The circular measure to seven places of deci- 
mals of the arc of the angle of the moon's parallax 
of 57' 5" is 0166048. 

2. The linear measure of the tangent of the angle 
of the parallax, with seven ciphers annexed, is 
3,963.0000000. 

Demonstratio7i by Division. — 3,963.0000000-^- 
0166048^238,605 miles, v^hich is the moon's mean 
distance. 

Distance of the Sun by Division. 

1. The circular measure to twelve places of 
decimals of the arc of the angle of the sun's paral- 
lax of 8".6, is 000041693976. 

2. The linear measure of the tangent of the 
angle of the parallax, with twelve ciphers annexed, 
is 3,963.000000000000. 

i)f;7^ow5^ra^^owJ^/Z)^^;mo^^.— 3,963.000000000000 
-^000041693976=:95,049,702 miles, which is the 
sun's mean distance. Compare these results with 
the mean distances of the sun and moon, found by 
a different process on p. 92. 

1. I have demonstrated how to find the diameter 
of any one of the heavenly bodies in the fourth 
term of a single proportion. 

2. I have shown how to determine the linear 
measure of the perpendicular leg of a right-angled 
triangle in the same way employed to find the 
semi-diameter of a circle, thus bringing within the 
reach of all a way to find the distances of the 
heavenly bodies by common arithmetic. 

3. By a very simple process in Division, I have 
resolved the distances indicated by the parallaxes of 
the moon and sun. 





\g 





THE STARS ARE WITHOUT PARALLAX. 



Circular Measure. 

A circle, whose radius is unity, the circular 
measure of its circumference retaining twelve 
places of decimals, is 6.283185307179=360°. 

The circular measure of an arc of one degree is 
0.017453292519. 

The circular measure of an arc of one second of 
a degree is 0.000290888208. The circular meas- 
ure of the arc of the parallax of any one of the 
heayenly bodies may be found, and the distance 
indicated by the parallax be determined by divi- 
sion, as in the given examples. 

My ambition in this department of science is 
satisfied. I had most earnestly desired, longed 
for, and labored to bring the solutions of these 
astronomical problems within the reach of all who 
understand common arithmetic. Having accom- 
plished this, I leave it to others to extend, by a 
little modification of my rule, the principle of find- 
ing the unknown perpendicular leg of any right- 
angled triangle, the linear measures of whose sine, 
arc, and tangent disagree in consequence of the 
largeness of the angle. 

The Stars are without Parallax. 

A near and fixed object will suffer no apparent 
displacement when viewed from a mere point (Hke 
it would if viewed from the extremities of a line) ; 
and ten or ten thousand observations from the 
same point would all be in the line of the visual 
ray of the first observation. So it is in all observa- 
tions made to determine stellar parallaxes. They 
are all in the line of the same visual ray that was 
first directed to a star to find its distance, and, 





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m 



THE STARS ARE WITHOUT PARALLAX. 



therefore, for the want of a Ime whose longitude 
would subtend an appreciable angle, the stars are 
of necessity without appreciable parallax. 

1. On p. 6, I have given the resulting distance 
of a star's annual parallax of 1" of a degree. The 
assumption shows that the distance to the nearest 
star can not be less than nearly forty trillions of 
miles, and how much further who can tell, for the 
stars, as it respects the annual motion of the earth, 
are without variableness, having no shadow of 
turning. 

2. The whole diameter of the earth's orbit, if 
compared with the line of a star's distance, is a 
mere point ; but the astronomers make the base 
line of their annual parallaxes but one-half of the 
diameter of the orbit of the earth, and consequent- 
ly but half a point. Now a mere point is without 
length, breadth, or thickness, being without- assign- 
able quantity ; and strange that but half of an 
unassignable quantity is the chosen base line of 
the astronomers. This being so relatively true, 
the. marvels of the astronomers' parallaxes of the 
stars, if true, involve a greater marvel, that, from 
a series of observations made from the extremities 
of but half a point, certain stars have been found 
to have a very appreciable quantity of parallax 
in angular measurements, varying from 0".046 to 
0".915. 

3. That the assertion, ''the whole diameter of the 
earth's orbit, when compared with the distance of 
a star, dwindles to a mere point," may be implicitly 
received as true, Burritt says : " The whole di- 
ameter of the orbit of Saturn (1,824,915,246 miles) 
is no thicker than a spider's web when compared 
with the distance of the stars.' 



«7C^ 




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THE EXAMINATION. 99 




The Examination. 

From what I have written, before I presented 
this portion of my work to be thought of by men, 
there can be : First, no mutual gravitation of the 
heavenly bodies among themselves. Seco?id, for 
the want of this mutual gravitation of the celestial 
spheres, the theory of the precession of the equi- 
noxes is without the ratification of nature. Third, 
the time and revolution of the sidereal year of the 
sun is baseless. Fourth, by the testimony of na- 
ture I will be able to establish the fact, that our 
earth, which is an oblate spheroid, revolves around 
the sun after the manner of a homogeneous and 
perfect sphere revolving around the sun, the den- 
sity of its matter not affected by the force of its 
axial rotation. Fifth, the variations of the astron- 
omers are wonderful ; and that the disciples of 
N^ewton, who are among the most highly gifted of 
the sons of earth, should have been so much out of 
the way, affords cause for a deliberate inquiry : 
What is truth ? 

But before we engage further in the grand con- 
flict, it will, without doubt, be pleasant to my 
readers to know that the system of astronomy 
which originated with Copernicus was enlarged 
and improved by Sh' Isaac Newton, and expound- 
ed, to the wondering delight of intelligent men and 
women, from age to age, is, by its friends and 
admirers, thought to be unimpeachable, and its 
collections of dogmas synonymous with a collection 
of the facts of nature. The words of Ferguson, 
Herschel, and Dick will best set forth their views. 

1. In Ferguson's Astronomy, p. 41, he says: 
'' Sir Isaac Newton has established this system on 
such an everlasting foundation of mathematical 







100 PRECESSION OF THE EQUINOCTIAL POINTS. 

and physical demonstration as never can be shaken, 
and none who understand him will hesitate about 
it.'' 

2. Herschel, in his Outlines of Astronomy^ p. 19, 
says : " There is now no danger of any revolution 
in astronomy like those which are daily changing 
the features of the less advanced sciences.'' 

3. In Dick's works, Vol. III., p. 25, he says : 
' ' The system broached by Copernicus, notwith- 
standing much opposition, soon made its way 
among the learned in Europe. It was afterward 
powerfully supported by the observations and rea- 
sonings of Gralileo, Kepler, Halley, Newton, La 
Place, and other celebrated philosophers, and now 
rests on a foundation firm and immutable as the 
laws of the universe." 

ISTow, not believing that the shaking of the 
Copernican system of astronomy is the same as 
shaking the true facts of nature, I advance in my 
work, and hope, as I have often prayed on this 
subject, to aim for the right way and the gain of 
the truth, and God defend and prosper me. 

"Precession of the Equinoctial. Points." 

PROPOSITION. 

Through the earth's annual motion round the 
sun, the stars seen from our earth do not change 
their points of rising, and the theory of the preces- 
sion of the equinoxes teaching they do, the tes- 
timony of nature is to be accepted ; and as such a 
phenomenon could only arise from the fact of the 
iarth preserving the invariability of its equinoctial 
points, I infer from this testimony of nature that 
there is nothing in nature to warrant the conclu- 



Ik 





THE PSEUDO SIDEREAL YEAR OF THE SUN, 101 



sion that the equinoctial points fall back, there is 
no "regress of the earth's nodes." 

The amount of the precession of the equinoxes is 
said to be 50". 1 of a degree every year ; and were 
the theory as much a fact of nature as it is supposed 
to be by learned astronomers, the stars would 
change their points of rising 50".l of a degree every 
year ; and a star, which in A. D. 1858 rose in the 
plane of the celestial equator, would in A. D. 1868 
rise 8' 21" east of the celestial equator. But a star, 
and all stars which this year describe the circle, of 
the celestial equator, and circles parallel to and 
declining to either side of it, describe the same di- 
urnal circles which they appeared to do last year, 
or ten years ago. This unanimous verdict of the 
invariability of the whole starry host, 'is nature's 
decisive refutation of the theory of the precession 
of the equinoxes. 

The Pseudo Sidereal Year of the Sun. 

Webster, under the word year : — " Sidereal year; 
the time in which the sun, departing from any fixed 
star, returns to the same. This is 365 days, 6 
hours, 9 minutes, 9.6 seconds." 

The astronomers and lexicographers are unani- 
mous in their opinions as to the time and existence 
of their sidereal year of the sun, but the times of the 
real and apparent revolutions of the heavenly 
bodies fully demonstrate the fallacy of the so-called 
" sun's sidereal year." At a time when the centres 
of the earth, sun, and a star are in a straight line, 
let the time and revolution of the apparent yearly 
sun begin by the star', and because of the apparent 
diurnal motion of the stars in the time of 23 hours, 
56 minutes, 4.09 seconds, at the close of the time 
of the yearly revolution, when the centres of the 

^ — — OB^ 






w'»^ 




.4SC : ca^ 



THE CAUSE OF KEPLER's FAILURE. 



earth, sun, and star should be in the same straight 
Hne, the star will be advanced 92° + beyond the line. 
Hence, because the time of the astronomers' sidereal 
year of the sun is not a multiple of the time of the 
apparent diurnal revolutions of the stars, their 
sidereal year of the sun exists not in nature. 

The Pseudo Sidereal Revolution of the Earth. 

Because the stars have apparent diurnal motion, 
and the time of the yearly revolution of the earth 
is not a multiple of the time of the diurnal revolu- 
tions of the stars ; all revolutions of heavenly bodies 
based on a fixed star are false. 

In Herschel's Outlines of Astronomy, p. 202, lie 
says ; " The annual retreat of the equinox is 50".l, 
and this are is described by the sun in the ecliptic 
in 20 minutes, 19.9 seconds. By so much shorter 
is the periodical return of our seasons, than the 
true sidereal revolution of the earth round the sun.'' 

But the earth does not set out from a star in its 
journey round the sun ; the effect on the stars be- 
ing the same as if the orbital motion had no exist- 
ence, and therefore Herschel's "true sidereal revo- 
lution of the earth round the sun" is nothing more 
than his aberration from the facts of nature. 

The Cause of Kepler's Failure. 

It is known to all informed, that the sun and 
stars have perpetual apparent motions. When 
Kepler set about to found his sidereal revolutions 
of the planets, he excluded from his calculations 
the perpetual apparent diurnal motion of the stars, 
assumed their fixedness, and then from a fixed star 
laid the foundation for his sidereal revolutions of 
the planets. This exclusion of the apparent motion 
of the stars led to a false system ; and being con- 






^^ 





VARIATIONS OF THE ASTRONOMERS. 

trary to nature, the revolutions must b.e also con- 
trary to nature, having no place but in the assump- 
tion. Therefore, when Sir Isaac Newton, in his 
Principia, p. 388, says, " The periodic times with 
respect to the fixed stars," he is perpetually contra- 
dicted by the perpetual apparent motion of every 
star in the celestial sphere. 

Variations of the Astronomers. 

1. T. Dick says: "The effect of the regress of 
the equinoctial points, is to cause an apparent 
revolution of the stars around the poles of the 
ecliptic." 

2. Mattison, in his High School Astronomy/, p. 70, 
says: "The distant stars have no motion, real or 
apparent, around the poles of the ecliptic." 

3. The reader will observe, that what Dick or^ 
affirms, Mattison denies. ^ 

4. Burritt's G-eograplnj of the Heavens, p. 29, 
says: "Id consequence of the motion of the earth 
eastward in its orbit, the stars appear to have a 
motion westward." 

5. Mitchel's Popular Astronomy, p. 77, on the 
orbital motion of the earth, says: "Now the 
earth's centre in the space of one day and night, 
or during one rotation, actually passes over 
2,000,000 of miles ; and it w^ould seem as though 
this change of position would sensibly affect ^'^ 
return of our star to the meridian ; but such is the 
vast distance of the stars, that visual rays sent to 
the same star from the extremities of a base line of 
2,000,000 of miles in length, are absolutely paral- 
lel under the most searching instrumental scrutiny 
that man has been able to make." 

6. What Burritt affirms, Mitchel denies. 







/^3V'* 




^/€)\ 


»^^ 




^^( 


104 


VARIATIONS Oi^ THE ASTRONOMERS. 


'Ji 




7. Webster, in his Spelling Book, p. 144, says : 
"The earth turns every part of its surface to the 
sun once in twenty-four hours.'' Suppose Webster 
to have opened a school among the Indians of the 
far north, who had not seen the sun for more than 
a month. He informs his pupils that the learning 
of centuries has culminated in demonstrating the 
fact of the earth turning every part of its surface 
to the sun once in twenty-four hours. After such 
an announcement, Avho of the company would ap- 
pear to be the most stupid — the great American 
lexicographer, or his pupils ? They might inquire 
what earth is meant ; for surely this part, occupied 
by us, has not seen a ray of the sun for more than 
thirty times twenty-four hours. Contrary to this, 
the earth turns every part of its surface to the sun 
once in the time of 365 solar days, 5 hours, 48 
minutes, 48 seconds, and as is the difference be- 
tween the time of a solar day and solar year ; so 
great is the mistake of Webster. 

8. Burritt teaches : "The earth moves eastward 
in its journey round the sun.'' 

9. Dr. T, P. Jones, in his Conversations on Natu- 
ral PMlosopluj , p. 105, says: "The earth moves 
westward in its journey round the sun." 

10. In the mental romp led on by Humboldt, in 
his Cosmos, Yol. I., p. 88, he says : " Light travels 
one distance of Sirius in three years." 

11. Peters says : "The distance of Sirius from 
the earth is so great, that the time required for its 
light to reach us is fifteen years." 

12. Mitchel's Planetary and Stellar Worlds, p. 
211, says : "Stars of the first magnitude send us 
their light in about seventeen years." Among the 
stars of the first magnitude Sirius is numbered. 



^^ 





VARIATIONS OF THE ASTRONOMERS. 105 



13. "Henderson reached the conclusion, in his 
observations on Sirius, that it required twenty-one 
years and nine months for the hght of that star to 
reach the earth." 

14. From among the big thoughts I select : 
" Huyghens assumed the intrinsic brightness of 
Sirius to equal the sun." 

15. 0. M. Mitchel says : " Sirius is the brightest 
and probably the largest of the fixed stars, with a 
diameter of more than a million of miles." 

16. Wollaston says : "Sirius is equal to sixty- 
three suns." ' 

17. Humboldt says : "Arcturus is equal to 1,331 
suns." 

18. Herschel says : "The star Vega in Lyra is 
thirty-eight times the diameter of the sun, and its 
solid contents 67,872 times greater." 

19. Mattison outdoes these liliputian calcula- 
tions by saying : " The star 61 in the Swan is esti- 
mated to be 200,000,000 of miles in diameter." 
Not far from being 10,000,000 times larger than 
the sun. 

20. In Humboldt's Cosmos, Yol. lY., p. 120, on 
the sidereal revolutions of the planets, he says : 
" During such a revolution a planet passes through 
exactly 360^ in its course round the sun ;" and in 
this conclusion all astronomers rest. 

21. In Webster's Dictionary, under " Tropical 
Year, — The period occupied by the sun in passing 
from one tropic, or one equinox,, to the other. On 
account of the precession of the equinoxes, it is 
20 minutes, 20 seconds, shorter than the sidereal 
year;" and in arc, according to Herschel, 50". 1 
of a degree less than 360^^. In this difference all 
the astronomers are agreed. 



\ 







106 VARIATIONS OF THE ASTRONOMERS. 

22. The difference among the advocates of the 
sidereal and tropical revolutions of the sun is not 
calculated to produce a conviction of the infallible 
nature of their science, as will be made to appear, 
in that Ferguson and Burritt give to the apparent 
sun the same number of degrees in his tropical 
revolution that is given by Kepler, Newton, and 
Humboldt to a planet or the sun in their sidereal 
revolutions. 

23. In Ferguson's Astronomy, p. 152, he says : 
"The sun describes the whole ecliptic, or 360^ in 
a tropical year." It should be 50". 1 of a degree 
less than 360°. 

24. In Burritt's Geography of the Heavens, Part 
II., p. 114, he sa^^s : " The sun describes the whole 
ecliptic, or 360^^, in a tropical year." It should be 
50". 1 less than 360^. Thus confounding the side- 
real and tropical revolutions in degree. If the 
science had been true, the advocates were in these 
things mistaken, for the tropical revolution in de- 
gree should be 50".l of a degree less than the 
sidereal revolution ; but they were engaged in 
expounding a mere theory, as is abundantly evi- 
denced by the variations adduced. 

25. As there is no two returns of the centre of 
the sun or that of the earth to the same fixed star 
in the time in which the earth passes through ex- 
actly 360^ of orbital revolution, the sidereal, trop- 
ical, and equinoctial revolutions of the astronomers 
in time and degrees are confusion ; and their con- 
founding the tropical and sidereal revolutions wdth 
each other in degree gives no ilhimination to their 
infallible scheme, which they supposed consisted of 
a transcript of the facts of nature. 





3 — 







PARALLELISM OF THE EARTH's AXIS. 107 

Parallelism of the Earth's Axis. 

1. The earth is an oblate spheroid, and being 
carried around the sun by the effect of an original 
side wise impulse, and not by the sun's assumed 
attraction, revolves as if it were a homogeneous 
and perfect sphere, maintaining the invariability of 
its equinoctial points and the constancy of the 
poles of the heavens. 

2. The line of the earth's axis prolonged to the 
sphere of the stars is the axis of the heavens, 
around which the stars appear to revolve ; and in 
whatever part of its orbit the earth may be in, at 
either solstice or equinoctial point, the axis of the 
earth will coincide with the axis of the heavens. 

3. To this definition Herschel rigidly adheres in 
his Outlines of Astronomy, p. 192, for he says : ''In 
this annual motion of the earth its axis preserves 
at all times the same direction, as if the orbital 
motion had no existence, and is carried around 
parallel to itself, and pointing always to the same 
vanishing point in the sphere of the fixed stars." 

4. From this absolute parallelism Herschel, not 
nature, departs in his Outlines of Astronomy, p. 
172. He says : " It is found, then, that, in virtue 
of the uniform part of the motion of the pole, it 
describes a circle in the heavens around the pole of 
the ecliptic as a centre, keeping constantly at the 
same distance of 23^ 28' from it, in a direction 
from east to west, and with such a velocity that 
the angle described by it in this, its imaginary 
orbit, is 50".10." 

5. In Herschel's Treatise on Astronomy, third 
edition, p. 169, he says: "The bright star of the 
Lesser Bear, which we call the Pole Star, has not 
always been, nor will always continue to be, our 




T^ 



vug) " i'gsr 

■ — - C 








108 PJtRALLELISM OF TBE EARTH's AXIS. . 



cynosure ; at the time of the earliest catalogues it 
was 12^^ from the pole; it is now (1835, date of the 
edition) only 1° 24^, and will approach yet nearer.'' 

6. For the next twenty-four years the distance 
remained constant ; for in Herschel's Outlines of 
Astronomy, fourth edition, p. 173, he says: "The 
bright star of the Lesser Bear, which we call the 
Pole Star, has not always been, nor will always con- 
tinue to be, our cynosure ; at the time of the con- 
struction of the earliest catalogues it was 12° from 
the pole ; it is now (1859, date of the edition) only 
1° 24', and will approach yet nearer." So that, ac- 
cording to the statements of Herschel, from the 
time of the earliest catalogues to 1835 the dis- 
tance between the pole of the heavens and the 
bright star of the Lesser Bear was diminished 10° 
36' by a constant departure of the earth's axis from 
its parellelism. But from 1835 to 1859 the dis- 
tance was the same, preserving the parellelism of 
the earth's axis for a period of twenty-four years. 

7. In Bollin's Ancient History, Book I., p. 141, 
he says : "The poles of the heavens have remained 
the same for a period of three thousand years." 

8. Herschel teaches that the poles of the heavens 
go forward, as an effect of the precession of the 
equinoxes. 

9. Ferguson, in his Astronomy Explained on the 
Principles of Sir Isaac Newton, says: "The poles 
of the heavens, as an" effect of the precession of the 
equinoxes, fall backward." Place these extremely 
opposite motions of the same pole of the heavens 
along side of Burritt and Jones's opposite motions 
of the earth, and the faith and reason which will 
comprehend how the earth can move backward 
and forward in its orbit at the same time will have 



m 



" ^^T 



f^BT . . rag^ 



C 



PROPOSITION. — HYPOTHESIS. 109 

no trouble in explaining how the motion of the 
poles of the heavens can, at the same time, be in- 
variable, and in motion, in opposite directions. 

Proposition. 

The earth revolves aromid the sun the same as if 
it were a homogeneous and perfect sphere. If the 
Newtonian law of universal gravitation, admitted, 
as we will see subsequently, to be the weakest of 
all forces of attraction, the superior forces of the 
motion of the heavenly spheres would absolve them 
from all allegiance to the sun's attraction. For the 
better understanding of the argument, I am willing 
to admit the existence of all Newton claimed for 
his discovery, and then show that the mutual at- 
tractions of every atom of matter, and of the mass 
of every sphere, tends to a perfet equilibrium. 

Hypothesis. 

Suppose a homogeneous and perfect sphere, of a 
consistence not to be molded into the form of an 
oblate spheroid as an effect of axial rotation, of the 
size of the earth as nearly as may be, revolving 
around the sun as an effect of the assumed attrac-, 
tion of gravitation of the sun. 

According to ISTewton, there being no, redundant 
matter gathered at the equator of such a globe, its 
nodes will not regress, and its axial rotation will not 
be acted on by centripetal force, as is the case with 
'an oblate spheroid. 

1. Seen from the surface of such a globe follow- 
ing the earth round the sun, during the time of 
one or one hundred orbital revolutions, the stars 
will preserve the invariability of their points of 
rising, culminating, and setting. 

2. It i^ identically so with the stars seen from 





y^J 



^ 





_ ^^ 

HYPOTHESIS. I W 

our earth. The star watchers have kept their in- 
tense gaze on the rays of the twinkhng stars, and 
eagerly sought to know : Do the stars change their 
points of rising from day to day, from year to 
year? And to every inquiry, they have given an 
invariable shining, No ; never. 

3. The same conclusion was reached by 0. M. 
Mitchel, in his Popular Astronomy, p. 18 : "An ex- 
amination of the points of rising, culminating, and 
setting of the fixed stars, showed them to be abso- 
lutely invariable." Therefore, because the stars 
seen from the earth never change their points of 
rising, culminating, and setting, which phenomenon 
is authenticated by 0. M. Mitchel, this fact of na- 
ture is a demonstration that the earth moves round 
the sun, the same as if it were a homogeneous and 

,^ perfect sphere. 

4. The position of the earth when at one or the 
other of the equinoctial points, if the sun's attrac- 
tion of gravitation affects the earth, the attraction 
must be the same on the northern hemisphere that 
it is on the southern hemisphere, resulting in a per- 
fect equilibrium, the same as if the whole matter 
of the earth was absolutely balanced on its centre, 
preserving the parallelism of the axis and the con- 
stancy of the poles of the heavens. So when the 
earth is at either equinoctial point, the action of 
the gravity of the sun is the same as if the earth 
were a homogeneous and perfect sphere. 

5. The equatorial diameter of the earth equals 
7,926 miles, and its polar diameter 7,900 miles. 
Within the earth you may describe a perfect sphere, 
every diameter of which equals the earth's polar 
diameter. The excess of matter above the contents 
of this perfect sphere is thirteen miles, thick at the 








.^Sl ^ ^ Q^;. 

HYPOTHESIS. 

circumference of the equator, declining gradually 
from either side of it to both the poles, at which 
points it is 0. This excess of matter constitutes 
the difference between a perfect sphere and an ob- 
late spheroid, and on it (sometimes called the re- 
dundant or superabundant matter gathered at the 
equatorial regions) Newton supposed the attrac- 
tion of the sun acted to cause the equinoctial points 
to regress. This involves the novelty of the sun's 
attraction being greatest on small quantities of mat- 
ter, and least on greatest quantities of matter. 
Thus prepared with the quantities requisite to un- 
derstand the subject, suppose a ring of matter, of 
the consistence and mass of that portion of the 
earth included in the difference between its polar 
and equatorial diameters, revolving around the sun, 
having the inclination of its axis the same as that 
of the earth. 

, The equinoctial points of such a ring will, ac- 
cording to JSTewton, be continually regressive. 

Then at some distance from the ring, with a 
swifter motion, suppose a homogeneous and per- 
fect sphere to be revolving around the sun, of a 
size to fit within the ring, having the same inclina- 
tion of axis with the ring. 

Of such a sphere Newton says, in Principia^ p. 
214, Book I. : "And the inclination of the axis, or 
the velocity of the rotation, will not be changed by 
centripetal force.'' The sphere overtakes the ring, 
passes into it, and when the equator of the sphere 
touches the equator of the ring, they adhere, and 
instantly the force of the attraction of gravitation 
on the sphere to preserve the parallelism of its 
axis, assisted by the additional force of its axial 
rotation, overcomes the very small force of the 





TIBV/ ' 





HYPOTHESIS. 




attraction of gravitation on the ring to cause the 
regress of its equinoctial points, and henceforth, in 
the union of the ring and sphere, the now spheroid 
will move round the sun the same as if it was a 
homogeneous and perfect sphere. 

Corollary 1. The precession of the equinoxes 
assumes that the attraction of gravitation is 
stronger on that part of the earth thirteen miles 
deep at the equatorial regions, diminishing to at 
the poles, than it is on the contents of the sphere 
within it, whose diameter is 7,900 miles. This is 
unreasonable. 

Corollary 2. The precession of the equinoxes 
supposes that the force of the attraction of universal 
gravitation is more on one pound of matter of that 
part of the earth which constitutes its oblate form 
of matter, than it is on ten pounds of matter of its 
spherical contents under the same law ; and this 
proportion being much greater in relation to the 
matter of the earth, which gives it its oblate form, 
compared with the enormous amount included 
within the sphere whose ' diameter is 7,900 miles. 
By so much is the absurdity greater. 

Corollary 3. If the force of this attraction of uni- 
versal gravitation on the shell of an o^^g is more 
than it is on the contents of the ^gg within the 
shell, we may accept the Newtonian hypothesis 
that the shell of the earth (called so by Herschel) 
composing the oblate form of the earth, is more 
strongly attracted than the rest of the earth. But 
the hypothesis is so contrary to reason, lacking the 
verifications of nature, as to demand its exclusion 
from the pale of science. 




Nimj ~ — Tjap 



^^ 




/'riiVi 




^^C 


IF — 






jw 


AN ANTIC OP UNIVERSAL GRAVITATION. 


113 





The Tides. 

When the matter of our earth was started into 
motion round its axis, the forces to cause the tides 
were generated. The centrifugal force to cause 
the riso, and the centripetal force to cause the fall, 
of the waters. Hence the origin of the tides, and 
all observed true phenomena may be traced to the 
centrifugal and centripetal forces of the earth, 
every atom of its matter being perpetually sub- 
jected to these forces in the given case. 

On this affirmation I rest, in the consciousness of 
its entire truth ; for as I have demonstrated that 
all the known forces of nature pertaining to a 
heavenly body may be generated by' a single im- 
pulse, it results that nature, in her works, is 
independent of the dogma of universal gravitation.- 

An Antic of Universal Gravitation. 

It is assumed that from a given point the waters 
of a distant sphere may be urged in opposite 
directions. 

According to Sir Isaac Newton, the attraction of 
every particle of the matter of a sphere may be 
assumed to be lodged in the centre of the globe, 
and on this hypothesis let the centres of the earth, 
moon, and sun be in a straight line, the moon 
being between the earth and sun, and the mutual 
attractions of the three bodies exerted in the line 
of the conjunction of the earth, moon, and sun. 

From the centre of the earth in this line the 
attractions of the sun and moon are said to draw 
the waters of the earth toward them, causing a 
high tide on the side of the earth nearest to the 
sun and moon ; and the same attractions of the sun 
and moon are supposed to project in an opposite 

8 

. naa^ 




I 







.^SZ! 

114 APPARENT STELLAR MOTIONS. 



direction from the centre of the earth the waters, 
causing a high tide on this opposite side of the 
earth. But the assumptions involving, as they do, 
the theory that the whole of the attractions of the 
sun and moon in a given line may both pull and 
push a part of the matter from the centre of a 
third distant sphere in opposite directions, is an 
antic indeed, and too contrary to true wisdom to 
find a place in true philosophy. On one side of 
the earth there may be a high tide, in the time of 
the entire absence of the sun and moon, they for 
the time being on the other side of the earth ; and 
if on one side, why not on the other, for like 
causes produce like effects, and our conclusion is 
adverse to the received theory. 

Apparent Stellar Motions. 

The disciples of Newton and Copernicus are at 
fault in ascribing as an effect the apparent daily 
acceleration of the stars to the annual motion of 
the earth. 

In T. Dick's works, Yol. III., p. 19, under the 
caption, "Annual Motion of the Stars," speaking 
of the changes which the clusters of stars undergo 
from time to time, he says : "Those variations in 
the appearance of the stars lead to the conclusion 
that there is an apparent annual revolution of 
these luminaries.'' 

In Burritt's Geography of the Heavens, p. 29, he 
says : "In consequence of the earth's motion east- 
ward in its orbit, the stars seem to have a motion 
westward beside their apparent diurnal motion." 
This apparent annual revolution of the stars, like 
the apparent yearly revolution of the sun, T. Dick 
says, is due to the " annual revolution of the earth 






f! 
I 



/SaT'. 



'Taa^ 




CAUSE OF THE STARS' DAILY ACCELERATION. 




115 




around the sun." This conclusion is also main- 
tained by Burritt. That the astronomers were 
mistaken is made out in a most conclusive way by 
an appeal to the facts of nature. 

The amount of the mean daily acceleration of 
the stars westward is 59' 10". 68+, but the amount 
of arc which tliQ earth describes in its mean daily 
motion in its orbit is 59' 8". 33. Hen<?e the arc or 
angle described by the stars in their mean daily 
acceleration is 2". 35+ more than the arc described 
by the earth in its mean daily motion in its orbit. 
On this account, when the astronomers attribute 
the cause of the apparent yearly motion of the 
stars to the motion of the earth in its orbit, they 
stand impeached for want of the true knowledge 
of the facts of nature. 

Cause of the Stars' Daily Acceleration. 

An arc of the celestial equator appears to pass 
the meridian in the time of a moan solar day, equal 
to 360° 59' 10".68+, and but 360° in the time of a 
sidereal day. 

By using the time (24 hours) of a mean solar 
day as a standard of measurement, take the time 
of some mean niidnight, with a star on your me- 
ridian, and at the time of the next mean midnidit 
the star will be advanced beyond your meridian 
westward an amount of angular measurement equal 
to 59' 10". 68+. So from one mean midnight to 
another in the time of 365 mean solar days, by 
these arcs of 59' 10".68+, the stars will move east- 
ward presenting all the phenomena described by 
Dick in the time of 365 mean solar days, or which 
is the same, the time of 366 sidereal days, which is 
in time 6 hours, 9 minutes, 9.6 seconds less than 



\gav 











r^gP- 



116 CAUSE OP THE STARS' DAILY ACCELERATION. 

the time of the astronomers' year of the earth by 
the stars. 

If you were to determine the revolutions of the 
earth on its axis by a star, every time the earth 
made one exact revolution on its axis, the stars 
would finish a complete apparent sidereal day revo- 
lution around the axis of the heavens ; but when 
you extend the standard of time to that of a mean 
solar day, in consequence of it the stars will have 
a mean daily acceleration of 59' 10".68+ westward 
around the axis of the heavens, in addition to 360^ 
of apparent revolution arising from the motion of 
the earth on its axis, the same as in their diurnal 
motion. 

Therefore, the observed apparent annual motion 
of the stars, in the time of 365 solar days, is com- 
posed of the arcs of the mean daily acceleration of 
the stars, belonging to effects of the earth's axial 
motions transferred to the stars and mixed up with 
the diurnal motions, and may be made plain by the 
following : 

1 . The continual motion of the earth on its axis 
will cause the stars in appearance, to an observer, 
to have continual motion. 

2. If you take the time in which the earth makes 
one rotation on its axis, and make this, as the as- 
tronomers have done, a standard of time ; then, 
counting; the revolutions in consecutive order, the 
stars will appear to have consecutive diurnal revo- 
lution around the axis of the heavens, each consecu- 
tive revolution in the exact time in which the earth 
completes a revolution of 360^ on its axis. 

3. But if you, as before stated, take the time ol 
a mean solar day, and periods of from midnight to 
midnight, to watch the stars and conform their mo- 











f^^ 




LAW OP PLANETARY MOTION. 





tions to the standard of time, the mean daily accel- 
erations of the stars will give them a westward mo- 
tion every day, increasing by the addition of an 
arc of 59' 10".68+, resulting in this : That if on 
the mean midnight of yom' own selection^ you find 
a star on your meridian at the next midnight, it 
will be advanced westward 69' 10". 68+, and in the 
lapse of 365 solar days the star will be on the me- 
ridian again. 

The astronomers have made a mistake in not 
noticing that the time of a mean solar day, if ap- 
plied to the stars, would generate their apparent 
mean daily acceleration ; but attributing it to the 
mean daily motion of the earth in its orbit, and not 
perceiving it to arise from the motion of the earth 
on its axis for the time of a mean solar day, they 
left the way open for me to show the true way to 
the children of men. ?S 



Law of Planetary Motion. 

The planets do not go round the stars like they 
do round the sun. On this account, when the area 
of the orbit of the planet is known to be a mere 
point when compared with the stellar distances, the 
effect of the orbital motion of the planet on the 
stars is the same as if the orbital motion had no 
existence. This agrees with the appearances of 
nature, and, therefore, the number of the apparent 
revolutions of the stars (366i) seen from the earth 
will be one less (equaling the number of axial ro- 
tations) than the number of the revolutions of the 
earth for the time oP its solar year, which are 3671, 
exactly the number of times the earth turns on its 
axis by a star, and revolves raund the sun. 

"^sc — ■ ■ 





^gaP 





THE astronomers' ANNUAL PARALLAXES. 



The Astponomeps' Annual Parallaxes. 

In the Smithsonian Report for 1858 p. 135, is 
given certain parallaxes, varying from 0".915 of a 
degree, to 0".046 of a degree. The Smithsonian 
Report is not inferior in authority and correctness, 
so far as it m6ves in concert with all institutions of 
learning ; but I prefer to quote and refer to it, 
rather than any other, because the Institution was 
originated as a specialty for the diffusion of knowl- 
edge among men. I especially invite the very 
particular attention of the President, Officers, Board 
of Regents, and the learned Secretary of the Smith- 
sonian Institution to a careful examination of my 
claims, lest others of their countrymen, less honor- 
able in fame and position, step in before them in 
acknowledging the facts of God in nafcure. 

Bessel's Annual Papallax of 61 Cygni, is 0".348. 

{From Smithsonian Report for 1858, p. 135.) 

Those who accept this parallax as probably true, 
should take enough interest in the subject to learn 
that the given distance indicated by it in the Re- 
port, instead of being equal to the distance over 
which a ray of light would move in 9.4 years, 
should be nearly 19 years. All the astronomers' 
parallaxes are vitiated by a like quantity, in con- 
sequence of their bisecting the isosceles triangle 
projected in the parallax, taking but one-half of 
the base line, without correspondingly reducing the 
measured parallax a like quantity. 

If a star seen from the extremities of the diame- 
ter of the earth's orbit suffers an apparent displace- 
ment of 2" of a degree, the distance indicated by it 
would be about twenty trillions of miles. But if 
you bisect the isosceles triangle, and take the semi- 





W^ 



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iS£l ■ C»i> 

THE astronomers' ANNUAL PARALLAXES. 119 

diameter of the earth's orbit for the base line, and 
also for the angular subtense of the parallax, as is 
done in the Smithsonian Report for 1858, p. 132, 
the resulting distance will be about twenty trillions 
of miles, the same as when the conditions involved 
the whole of the diameter of the earth's orbit for 
the base line of 2" of parallax. But I propose the 
true and whole diameter of the earth's orbit to be 
used as a base line of an annual parallax, as defined 
by. Webster, and from its extremities it is assumed 
that a star seen had an annual parallax of 1" of a 
degree, and trigonometrically, or by my new 
methods by simple proportion and division, the re- 
sult will be the same, about forty trillions of miles, 
or twice as much as is given by the astronomers. 
This is what I mean when I say that the manner 
of the astronomers in bisecting their annual paral- 
laxes lead to but half the true result. 

JNTow, I have given an annual parallax of 1", and 
if you will, you may bisect the isosceles triangle of 
the parallax after the manner of that to which I 
have referred you in the Smithsonian Report ; and 
also bisect the angle of the parallax v/hich was 
subtended by the diameter of the earth's orbit, 
and the result will be, as before, about forty tril- 
lions of miles, twice as far as the men of science 
have heretofore thought the distance of the stars 
was from an annual parallax of one second of a 
degree. I will now particularly notice Bessers 
annual parallax of 61 Cygni, it being 0".348 of a 
degree. Wishing to place the argument on the 
most solid foundation, becoming the dignity of the 
subject and the fame of the discoverer, I will place 
before the reader what is said about the base line 
of annual parallaxes in the Smithsonian Report for 



^3 ' • jT 





,^s?. 





THE DIFFERENCE BETWEEN THEORY AND FACTS. 



1858, p. 132 : ''Our change*of position, involving 
a distance of more than 200,000,000 of miles, 
dwindles down to nothing in comparison with the 
line which extends from the earth to the stars.'' 
Admit this, and then the base line of Bessel's 
parallax was nothing, and the parallax must have 
been 0".00.0 also. 

Axiom. 

The star 61 in the Swan was observed from a 
mere point, and such observations culminated in 
a point ; and hence any amount of an appreciable 
parallax, when the extent of field of observation 
admitted of no other extension than could be 
afforded from a mere point, was impossible. 

When, in addition to this, you take into consid- 
eration that Bessel's observations of 61 Cygni were 
at all times complicated by the diurnal and sup- 
posed annual aberration of the light of the stars, 
by the assumed precession of the equinoxes, the 
nutation of the earth's axis, the refraction of light, 
and the deflection of the light of the stars as it 
enters our atmosphere, the probabilities of the 
truth of his parallax have vanished away. • 

Peters* Annual Parallax of Capella is 0".046. 

The annual parallax of the star Capella, by 
Peters, printed in the Smithsonian Report for 
1858, p. 135, is 0".046 of a degree, and the time 
required for its light to reach us is said to be 71.7 
years. 

The Difference Between Theory and Facts. 

A parallax of 0".046 of a degree, seen from the 
extremities of the diameter of the earth's orbit, in- 



''^acr 






i§ 






THE DIFFERENCE BETWEEN THEORY AND FACTS. 121 

dicates a distance forty-two times greater than that 
of HerscheFs annual parallax of 1" of a degree, 
as set forth in the fourth edition of his Outlines of 
Astronomy, p. 456, and light would require a 
period of over 140 years to pass over the distance. 
Reduce the line of the diameter of the earth's orbit 
to a yard, and Herschel's resulting distance from a 
parallax of 1" of a degree in the same proportion, 
and their relation to each other is as one yard to 
sixty miles nearly. 

Again : with the diameter of the earth's orbit 
reduced to a yard, and the distance indicated by 
Peters' annual parallax of the star Capella in the 
same proportion, and the . relation they bear to 
each other is as one yard to 2,520 miles. This 
analysis clearly aids ordinary minds to readily 
perceive that these things being so, the proportions 
at once lead to the conclusion that all such annual 
parallaxes are merely theoretical. 

Does not this comparison place the annual paral- 
laxes in so forlorn an estate as to render their 
acceptance as facts of nature impossible, they 
appearing more like impositions in science than 
beautiful developments of natural truth ? - 

1. The parallax of the star Capella indicates a 
distance of over 850,000,000,000,000 of miles, 
which is about twice the distance allowed for in 
the Smithsonian Report. 

2. The distance indicated by the parallax of the 
star Capella is forty- two times greater than Her- 
schel's annual parallax of 1", and is twice the 
quantity allowed for in the Smithsonian Report. 

3. Light is known to travel at the rate of 
192,000 miles each second of time, and at this % 
rate it would require over 140 years for the light 









122 • UNIVERSAL GRAVITATION. 

of the star to reach the earth — twice as long as is 
allowed for in the Smithsonian Report. 

4. Because visual rays directed from the ex- 
tremities of the diameter of the earth's orbit to a 
star, supposed to be 19,788,239,040,000 of miles 
from the earth, will coincide and be the same with 
respect to the star, it becomes a monstrosity in 
science to suppose that at forty-two times the dis- 
tance the visual rays of the observer will cross each 
other, and subtend a parallax of 0".046 of a degree. 
Or you may discount the half of the calculation, 
and get down to that of the Smithsonian Report, 
and the same fact concerning the law of distance 
cuts off all hope of obtaining an annual parallax. 
You may make another discount of one -half, and 
get far below the calculation of the Smithsonian 
Report, and still there comes, from the profound, 
unfathomable distance, no hope for annual paral- 
laxes. 

Universal Gravitation. 

In the Smithsonian Report for 1856, p. 200, it 
says : ''Newton's theory of universal gravitation : 
the most extended generalization ever established 
by man. It may be expressed as follows : 

"1. The attraction exists between the atoms of 
all matter at finite distances, and is the same for 
all kinds of matter ; hence, 

"2. The force of attraction is proportional to the 
mass of the attracting body, the distance being the 
same. 

''3. If the same body attracts several bodies at 
different distances, the forces are inversely as the 
square of the distances. 

"All deductions from this theory are in strict 



TS^ 




Z^^i 





EXTENT OF THE SUN^S ATTRACTION. 123 

accordance with the phenomena of nature. The 
only proof of the truth of any physical law.'' 

At this point I join issue with the scheme, and 
say : Because the truly understood phenomena of 
nature is in strict disaccordance with the deduc- 
tions from the theory of universal gravitation, it 
can not be true. And because the assumed attrac- 
tion of the sun is capable of carrying around the 
sun in orbits as many bodies as can be placed side 
by side, in as many orbits as can be described in 
the bounds of the system of the sun, this repletion 
is too much for the theory as heretofore expounded 
to endure ; and this being too much, exposes its own 
fallacy. 

The Assumed Quantity of the Sun's Attraction. 

The force of the attraction of the sun has been 
estimated to be between five and seven hundred 
times more than all the forces of all the other 
bodies of the solar system ; but I am prepared to 
prove that the sun is as capable of carrying a num- 
ber more than a thousand times greater than all 
the bodies which are now assumed to be carried 
round the sun by his own attraction, as he is capa- 
ble of carrying Mercury alone by the theory. 

Extent of the Sun's Attraction. 

From every point of the surface of the sun radi- 
ating into space the light of the sun goes forth, ex- 
tending beyond the orbit of Neptune, the light 
decreasing in intensity as the square of the distance 
increases. 

So the attraction of gravitation from every point 
of the surface of the sun, it is said, goes forth, and 
extends beyond the orbit of Neptune, decreasing 
in intensity as the square of the distance increases, 





' ^m^ 





^mm 



ILLUSTRATION. 





and thus it appears that the disciples of Newton 
hold that a like law which obtains in nature in re- 
spect to the light of the sun, holds good in respect 
to their assumed dogma of the attraction of the 
gravity of the sun. 

Furthermore, you are not to suppose that the 
mutual gravitation of a planet and the sun are 
gathered up and follow the planet round the sun ; 
but like as a body or planet moves in the vast field 
or ocean of the sun's light, or like a fish moves 
through the water, or a bird moves through the 
air, so a heavenly body moves through the vast 
field of the sun's attraction of gravitation, which 
has been assumed to be coequal with the extent of 
the light of the sun, and governed by the same law 
of the square of the distance. 

You are also to conclude that the sun's attrac- 
tion of gravitation is not arrested by the density of 
a heavenly body, as the light of the sun is ; but, ac- 
cording to the theory, it passes through a body, 
however dense it may be, with as much freedom 
as if the space occupied by the planet was free from 
every obstruction, and to suppose otherwise, would 
in the event of a conjunction of all the planets, 
tumble the theory of universal gravitation into in- 
extricable confusion. 

Illustration. 

Divide the area of the orbit of the earth into as 
many angles or parts as may be subtended by the 
equatorial diameter of the earth, seen from the 
centre of the sun. In every one of these angles or 
parts the attraction of gravity of the sun is supposed 
to be always present, the same as is the sun's light, 
the former to move the earth, the latter for its illu- 



^^ 




ILLUSTRATION. 




mination, without any respect to the presence or 
absence of the earth. All of the Newtonian phi- 
losophy are free to admit the sufficiency of the 
force of the sun's attraction to carry the earth over 
any one of these angles or parts, in the earth's jour- 
ney through the vast ocean of the attraction of 
gravitation ; and if so, why not sufficient to carry a 
globe of the size and mass of the earth, placed in 
every one of these angles in a revolution round the 
sun ? In this attraction of the sun on the planets, 
the astronomers have perpetrated a darling error 
in assuming to weigh the sun against the planets 
on an imaginary steelyard or balance, and on such 
a basis they have computed the weight of the bodies 
of the solar system, and made it the measure of the 
mutual attractions of all the bodies revolving around 
the sun. Admit the astronomers' law in this case, 
and at a time when the planets are in conjunction, 
if then they can be weighed against the sun, by the 
same reasons a like experiment may be tried on the 
opposite side of the sun with another imaginary 
steelyard or balance, and another set of planets 
like those first weighed, and the result must be the 
same. So you may project as many radii from the 
sun's centre to the outmost bounds of the solar sys- 
tem as the circular space will admit of, to accom- 
modate the diameters of the planets. Use these 
radii as imaginary steelyards or balances, place on 
every one of them bodies exactly like the planets, 
of the same number, and simultaneously they may 
all be weighed against the sun without any more 
disturbing his force or position than would the 
weighing of the planets alone against the sun, and 
with the same imaginary result. 

Now select one of the angles into which the area 










ILLUSTRATION. 




of the earth's orbit was divided, and let it be the one 
beginning with the vernal equinoctial point ; and as 
the earth moves out of this angle, the force does not 
move along with it, but remains in the angle, and 
is as potent to move a second and third earth fol- 
lowing the first as it was the first one. So on add 
globe to globe in consecutive order, until the sun is 
surrounded with a ring of globes of the size and 
density of our earth, and the force of the sun's at- 
traction to cause the orbital motion of the earth is 
also suj3icient, because of its abiding force over the 
whole orbit, to carry this ring of globes round the 
sun in continual orbital motion. Deny this, and 
you deny the doctrine of universal gravitation. 
Call to mind the spherical space illuminated by the 
sun, the outskirts of which are far beyond the orbit 
of Neptune, and at every point within it there is 
assumed to be continually present some force of 
the sun's attraction, as intense as when at first the 
primordial laws of the universe were called into 
requisition by the Creator. Some have thought 
that Mercury is as dense as lead, and the planets 
outward are decreased in density, so that the den- 
sity of the matter of the planet Neptune equals the 
density of cork. With some such scale of decreas- 
ing density over the square of the distance from the 
sun, suppose at every point within the solar sys- 
tem an atom of matter to be present, and the atoms 
free to move among themselves. Now let every 
one of these atoms of the density of lead at Mercu- 
ry's, distance, decreasing to the density of cork at 
Neptune's distance, from the sun, be subjected to 
the Newtonian projectile and centripetal forces, and 
for the reason, if it be the sun's attraction that car- 
ries the planets around tlie sun, the same force is 



^ 






UNI\^ERSAL GRAVITATION. 127 [^ 

^ M 

sufficient to carry every one of these atoms round 
the sun, because the force of gravitation in unwasted 
energy is assumed to be ever present at every point 
of the spherical space of the solar system. This is 
so much more than the system of weighing the 
sun against the planets can endure, that it, and all 
that is related to it, should be abandoned for a 
better way of knowledge. 

Universal Gravitation. . 

The Smithsonian Report for 1856 defines the 
attraction of gravitation to be, "(46) The recip- 
rocal tendency of all parts of the solar system to 
approach each other;" and, *'(50) Gravitation the 
most feeble of all attractions." 

1. Of the bodies of the solar system this can not 
be true, because the forces of the axial and orbital 
revolutions of the spheres are greater than the cal- 
culated gravitation of the spheres among themselves. 

2. On p. 18 there is an experiment to show how 
a certain quantity of matter may or may not be 
under the action of the gravitation of the sphere. 
Such is the nature or effect of axial rotation, that 
any forces exterior to the rotating heavenly body 
are abundantly overcome by it, securing the stabil- 
ity of the motion of the body. 

3. All error carries with it the seeds of its own 
dissolution, the means of its own refutation. The 
admission that the force of gravitation is the most 
feeble of all attractions, is weakness indeed. Weak- 
ness to such an amount as is worthy to be lost 
sight of in calculating and accounting for the forces 
of nature to move the heavenly bodies, unless you 
assume that a weak force overcomes a stronger 
one, which is absurd. 





<gnn ^S&i^ 

THE CROWN IN VIEW. 



The Crown in View. 

{Smithsonian Report for 1856, p. 201.) 

" (52) The earth is nearly a sphere, and all 
bodies fall in straight lines, directed nearly to its 
centre.'' 

What a fruit of cultivated ignorance, and the 
evidence of how the noble in intellect servilely 
follow tradition ! There was a time when, on the 
descent of bodies, the students of nature were 
divided in opinion ; some claiming that all motion 
was originally and naturally curvilinear ; and others, 
that all motion was naturally and originally recti- 
linear. This latter opinion, though contrary to 
nature, prevailed ; and now, without a true why 
2^ or wherefore, even the learned Secretary of the 
^^ Smithsonian Institution avows this error for truth, 
^ I when all the phenomena of nature, the only proof 

OF THE TRUTH OF ANY PHYSICAL LAW, are OppOScd to 

his teaching. 

That bodies do not fall in straight lines, directed 
nearly to the centre of the earth, or as others 
teach, directed exactly to the centre of the earth 
(for the scholars are not agreed), is demonstrated 
by the fall of meteors, and also by the descent to 
the earth of all kinds of projectiles, they universally 
and invariably describe curve lines in their descent, 
being subject to the forces of the earth's motions, 
from the force of which they can not escape. And 
because in the phenomena of nature there is no 
true record of the observed right-line motion of 
any body, the law of straight-line motion, taught 
in the Smithsonian Report, is not consonant with 
the facts of nature, and therefore not true. 

The hypothesis of universal gravitation endows 



71 





fl 



^Sl. 



JSS^ 



THE CROWN IN VIEW. 



every atom of matter with power to move itself. 
This is contrary to nature, matter being aUke indif- 
ferent to rest or motion, its perfect passivity being 
originally necessary to permit of its being moved ; 
and when started into motion aromid the axis of 
each one of the heavenly bodies, then, and not 
before, arose the attraction of the matter of the 
sphere to its axial centre. Hence the origin of 
the gravitation of the matter of each one of the 
heavenly bodies ; and being confined to the sphere 
and its atmosphere, the natural, proper, and signifi- 
cant name of it is Spheroidal Gravitation. 

This spheroidal gravitation, in its effects, was 
seen by Sir Isaac Newton, but not understood by 
him ; and hence, instead of attributing the descent 
of bodies to the earth, and the tendency of every 
particle of the matter of the earth, to the attracting 
tendency of the earth's axial rotation, the earth's 
true centripetal force, he supposed an unseen 
power, to himself, as he confesses, perfectly incom- 
prehensible, to draw all the particles of the matter 
of the earth to its centre. He then stamped every 
particle of all the matter in the universe with this 
mistakQ, and originated his now universally re- 
ceived doctrine of universal gravitation. Had he 
known that from a single impulse a globe could be 
urged in the direction of a curve line, some of the 
labor of the Principia would have been expended 
in another theory of the celestial motions. 

I have shown, on p. 73, that from a projectile 
impulse a globe may be urged in the direction of 
a curve line ; and such a demonstration led me to 
the conclusion, that the same kind of force would 
turn a planet on its axis, and urge it forward over 
an arc of its orbit ; and because the curve-line 
9 




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THE CROWN IN VIEW. 



motion of a globe arising from a single impulse 
may be more or less curved, so as to agree with 
the curve of any circle, ellipse, or epicycle, it be- 
came evident to me that all the directions of 
motions and varieties of orbits in which the 
heavenly bodies are known to move were origin- 
ated by single impulses, and these discoveries 
originated the right, tjie authority, and duty to 
say to mankind : Behold the way of the Lord in 
nature ! 








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